What I’ve learned in APPC so far

“If you know how to explain something, you truly understand it,” to quote my dad, each time I discuss with him before a test. “Scientists have found that if you explain things (aloud), you remember them better,” to quote my English teacher.

With that, here are the major topics I’ve learned in APPC from week #1 and week #2.

Concavity

Concavity is the curve of a graph. The best way to think of it is a parabola that grows more quadratic/exponential.

There is a simple way to tell the concavity of the graph, which is by drawing a little smiley face. If it’s smiling, it’s up! If it’s sad, it’s down :(

Increasing vs. Decreasing

This one can be confusing but consider it a separate thing to concavity. Like, the concavity is the ice cream, and increasing/decreasing is the cone/cup.

When the slope (or the rate the line is changing) is positive, it’s going up, then it’s increasing, and vice versa.

Finding the rate of change

f(x)-f(x) // x -- x

This is the formula. It’s a long process, stay with me.

1. You’ll get your two x values, and you will plug it in to your given equation. The x values will be formatted like an x,y but with [] brackets. [5,6]
2. You’ll get your two y values. (5, 3) (6, 7).
3. You’ll plug these values into the formula.

   7-3 // 6-5
   

4. You’ll simplify and get your rate of change.

   4 // 1 = 4/1 = 4
   

   And yeah! With this formula, you can alos backtrack if you don’t get the numbers I listed, I just listed the traditional equation.